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Towards end-to-end likelihood-free inference with convolutional neural networks.
British Journal of Mathematical and Statistical Psychology ( IF 1.5 ) Pub Date : 2019-02-22 , DOI: 10.1111/bmsp.12159
Stefan T Radev 1 , Ulf K Mertens 1 , Andreas Voss 1 , Ullrich Köthe 2
Affiliation  

Complex simulator‐based models with non‐standard sampling distributions require sophisticated design choices for reliable approximate parameter inference. We introduce a fast, end‐to‐end approach for approximate Bayesian computation (ABC) based on fully convolutional neural networks. The method enables users of ABC to derive simultaneously the posterior mean and variance of multidimensional posterior distributions directly from raw simulated data. Once trained on simulated data, the convolutional neural network is able to map real data samples of variable size to the first two posterior moments of the relevant parameter's distributions. Thus, in contrast to other machine learning approaches to ABC, our approach allows us to generate reusable models that can be applied by different researchers employing the same model. We verify the utility of our method on two common statistical models (i.e., a multivariate normal distribution and a multiple regression scenario), for which the posterior parameter distributions can be derived analytically. We then apply our method to recover the parameters of the leaky competing accumulator (LCA) model and we reference our results to the current state‐of‐the‐art technique, which is the probability density estimation (PDA). Results show that our method exhibits a lower approximation error compared with other machine learning approaches to ABC. It also performs similarly to PDA in recovering the parameters of the LCA model.

中文翻译:

借助卷积神经网络实现端到端的无似然推理。

具有非标准采样分布的复杂的基于仿真器的模型需要复杂的设计选择,以实现可靠的近似参数推断。我们介绍了一种基于完全卷积神经网络的快速,端到端的近似贝叶斯计算(ABC)方法。该方法使ABC的用户可以直接从原始模拟数据中同时导出多维后验分布的后验均值和方差。一旦在模拟数据上进行训练,卷积神经网络就能够将大小可变的真实数据样本映射到相关参数分布的前两个后矩。因此,与其他针对ABC的机器学习方法相反,我们的方法允许我们生成可重用的模型,这些模型可被采用同一模型的不同研究人员应用。我们在两种常见的统计模型(即多元正态分布和多元回归情景)上验证了我们方法的实用性,对于这些模型,可以分析得出后验参数分布。然后,我们将我们的方法用于恢复泄漏竞争累加器(LCA)模型的参数,并将我们的结果参考当前的最新技术,即概率密度估计(PDA)。结果表明,与其他针对ABC的机器学习方法相比,我们的方法显示出较低的逼近误差。在恢复LCA模型的参数方面,它的性能与PDA类似。然后,我们将我们的方法用于恢复泄漏竞争累加器(LCA)模型的参数,并将我们的结果参考当前的最新技术,即概率密度估计(PDA)。结果表明,与其他针对ABC的机器学习方法相比,我们的方法显示出较低的逼近误差。在恢复LCA模型的参数方面,它的性能与PDA类似。然后,我们将我们的方法用于恢复泄漏竞争累加器(LCA)模型的参数,并将我们的结果参考当前的最新技术,即概率密度估计(PDA)。结果表明,与其他针对ABC的机器学习方法相比,我们的方法显示出较低的逼近误差。在恢复LCA模型的参数方面,它的性能与PDA类似。
更新日期:2019-02-22
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